1. Field of the Invention
The present invention relates to the field of signal processing in a channel, and, in particular, to signal processing in a partial response channel.
2. Background
In magnetic recording devices, such as magnetic disks and tapes, a recording head is used to read and write information to and from a magnetic surface. In a typical rotating medium-based storage system, data is stored on magnetic disks in a series of concentric "tracks." These tracks are accessed by a read/write head that detects variations in the magnetic orientation of the disk surface. The read/write head moves back and forth radially on the disk under control of a head-positioning servo mechanism so that it can be selectively positioned over a selected one of the tracks. Once in position over a track, the servo mechanism causes the head to trace a path that follows the center line of the selected track.
Generally, the inductive recording head consists of a slit toroid made up of high permeability magnetic material and wound by several conductor turns. The toroid contains a gap which is positioned over the data tracks on the magnetic recording surface. To record, a current is generated through the conductor windings, altering the magnetic field in the toroid. At the location of the gap, the amplitude of the magnetic field is large enough to record on the magnetic material of the storage device to a sufficient depth. The amplitude of the magnetic field falls off sharply away from the gap.
By manipulating the current through the conductor windings, the magnitude and direction of the magnetic flux at the location of the gap can be modulated in such a fashion as to encode information into the magnetic surface of the storage device. A pattern of external and internal fields are created as the head and recording surface are moved relative to each other. These patterns are similar to a series of bar magnets of changing polarities. The polarity transitions are then readable as transitions in the magnetic flux at the recording surface. In read mode, as the magnetic storage surface moves across the gap in the head, the magnetic field of the storage surface is detected at the gap, and a voltage is induced in the coil proportional to the rate of change of the flux. The read channel then processes this analog voltage signal, typically converting the flux transitions into a series of pulses, and converts the analog signal into digital data.
Magnetic storage devices sometimes use analog peak detection to process incoming read signals. However, as recording density, or "user density" (Du), increases the analog peak detection scheme becomes unreliable because of the large amount of inter-symbol interference (ISI) between adjacent pulses. Alternatively, a partial response maximum likelihood (PRML) channel can be used to increase the user density. However, this method requires very good equalization of the read signal to shape the read signal into the desired partial response (PR) target waveform.
User density (D.sub.u) is a measure of how the pulse width relates to the data rate in the form of a ratio of the analog signal pulse-width at 50% magnitude over the length of the data period. A higher user density means that signal pulses resulting from read transitions are spread over a larger number of clock cycles, increasing the interaction or overlap of adjacent pulses, and resulting in greater ISI.
A partial response channel does not remove ISI from the channel signal. Instead, the signal is equalized to provide a target pulse waveform having predefined values at specific sampling instants. The effects of ISI on the target pulse waveform are predicted and incorporated into a pulse detection scheme which determines the occurrence of a signal pulse based on the sample history of the waveform and model waveform prediction. The history of the sample waveform is matched to a set of model waveforms, and the most likely model waveform is used to decode the signal into binary data. Hence, it is often referred to as "maximum likelihood" detection.
Partial response channels are therefore more robust than analog peak detectors in the presence of ISI. However, as described below, a problem exists in PR channels due to the equalization required to generate the target pulse waveform, as well as the process used to generate a signal metric for determining the most likely waveform. The PR equalizer and ML estimator used to generate the signal metric each serve to correlate noise in the channel. As a result, ML detector performance is impaired by a reduction in signal-to-noise gain.
The most commonly used maximum likelihood (ML) detector is the Viterbi detector, which is optimized for detection of signals in the presence of white noise. It is, however, somewhat complicated to implement especially for higher orders of PR channels (e.g. EPR4, EEPR4) and very inefficient for parallel/pipeline implementation architectures. Furthermore, its performance degrades as the noise become correlated. Look-ahead ML detector hardware requirements are usually less than that for a Viterbi detector, and look-ahead detectors are more suitable for parallel/pipeline implementation. However, the performance of look-ahead ML detectors is usually inferior to a Viterbi detector.
Look-ahead detectors are described in A. M. Patel's article "A New Digital Signal Processing Channel of Data Storage Products," Digest of the Magnetic Recording Conference, June 1991, pp. E6-E7; in A. M. Patel, et al., "Performance Data for a Six-Sample Look-Ahead (1.7) ML Detection Channel," IEEE Transactions on Magnetics, vol. 29, no. 6, pp. 4012-4014, November 1993; and in Patel's U.S. Pat. No. 4,945,538. A look-ahead detector is also described in U.S. Pat. No. 5,311,178 to T. Pan and R. G. Yamasaki.
The Patel and Pan/Yamasaki channels use partial response signaling to limit the number of isolated pulse non-zero samples. The Patel channel is equalized to EPR4 with three non-zero samples, and the Pan/Yamasaki channel is equalized to EEPR4 (or E.sup.2 PR4) where the four non-zero samples, .alpha., .beta., .beta. and .alpha., are 1, 3, 3 and 1, respectively. Both channels use the (1,7) RLL code to simplify signal detection.
Run-length limited (RLL) codes are useful because they place upper and lower bounds on the number of clock cycles occurring between transitions. The upper bound is very important because clock recovery is based on the occurrence of these transitions. For example, a long train of zeros in a data sequence produces no transitions and the clock recovery circuit has no input pulse with which to synchronize its tracking. In this situation, the data recovery timing might drift out of phase. RLL codes ensure that sufficient transitions occur for the clock recovery circuit to maintain the correct timing phase and frequency. Also, by maintaining the lower bound on the number of zeros between consecutive ones, signal pulses in the read channel are separated to reduce the intersymbol interference (ISI) caused by interaction between adjacent signal pulses.
The (1,7) RLL code is characterized by a minimum of one "0" and a maximum of seven "0's" between consecutive "1's". In the modified non-return-to-zero (NRZI) format, where each "1" is represented by a transition, and each "0" is represented by the lack of a transition, the (1,7) RLL code is sufficient for clock recovery purposes. Further, by maintaining the minimum of one "0" between consecutive "1's", transitions are separated so as to be differentiable from one another.
FIG. 1 illustrates, with solid curve 100, an isolated Lorentzian pulse equalized and sampled for EEPR4, and a minimum distance error event shown as a dashed curve 101. The pulse is the result of applying a positive unit step transition, e.g. a transition from a magnetic read head, to a (1-D)(1+D).sup.3 channel (EEPR4). The circles on solid waveform 100 show the isolated pulse samples for EEPR4. Samples of minimum distance error event 101 are indicated by diamonds. Minimum distance error event 101 is equivalent to the isolated pulse (100) shifted by one code period in time.
In most ML detectors, including the Viterbi detector, the square of the Euclidean distance between two sequences is often used as the signal metric. The Euclidean distance is defined as the square root of the sum of the squared error terms between two waveforms at each sampling instant. The squared Euclidean distance error of a sample combination is defined as: ##EQU1## where ya, yb, yc, yd and ye are the expected values for the model waveform; y.sub.0, y.sub.1, y.sub.2, y.sub.3 and y.sub.4 are consecutive sample values; and d.sub.i is the sample error at y.sub.i.
In FIG. 1, the isolated pulse waveform 100 and the minimum distance error event 101 have sample errors of values 0, 1, 2, 0, 2 and 1 for samples y.sub.M1, y.sub.0, y.sub.1, y.sub.2, y.sub.3 and y.sub.4, respectively, where y.sub.M1 is referred to as a look-back sample. The squared Euclidean distance between sampled waveform 100 and the minimum distance error event 101 is labeled d.sub.MIN.sup.2. d.sub.MIN.sup.2 is equal to the sum of the squares of these values, which adds up to a value of 10.
In the ML detector of U.S. Pat. No. 5,311,178, thresholds for each decision function are determined by minimizing the error between an expected sample model waveform and the nearest valid sample model waveform. For this reason, the thresholds for each function are dependent on the present state, as the next valid states are determined by the present state.
In the calculation of the Euclidean distance for use as a signal metric, for a first model waveform to be selected over a second model waveform, EQU E.sub.1.sup.2 -E.sub.2.sup.2 &lt;0 [2]
where E.sub.1.sup.2 is the squared Euclidean distance between the first model waveform and the sampled signal, and E.sub.2.sup.2 is the squared Euclidean distance between the second model waveform and the sampled signal. The squared terms of the sampled signal are canceled out to yield a linear decision function. This will generate the following threshold decision: EQU (ya.sub.2 -ya.sub.1)y.sub.0 +(yb.sub.2 -yb.sub.1)y.sub.1 +(yc.sub.2 -yc.sub.1)y.sub.2 +(yd.sub.2 -yd.sub.1)y.sub.3 +(ye.sub.2 -ye.sub.1)y.sub.4 &lt;(ya.sub.2 -ya.sub.1)(ya.sub.2 +ya.sub.1)+. . . +(ye.sub.2 -ye.sub.1)(ye.sub.2 +ye.sub.1) [3]
where y.sub.0, y.sub.1, y.sub.2, y.sub.3 and y.sub.4 are the actual sample values; ya.sub.1, yb.sub.1, yc.sub.1, yd.sub.1 and ye.sub.1 are the expected values for the first model waveform; and ya.sub.2, yb.sub.2, yc.sub.2, yd.sub.2 and ye.sub.2 are the expected values for the second model waveform.
For the sample points at which the model waveforms are equal, the products including the factor (yk.sub.2 -yk.sub.1), where k is the associated sample point, are canceled. In the negative phase, i.e. for negative transitions, the thresholds are the same, but the inequalities are reversed and the decision functions are multiplied by "-1".
The peak check decision functions from FIG. 5A of U.S. Pat. No. 5,311,178 are shown below for .alpha.=1 and .beta.=3. Fw (Fz in the patent) is normalized with a sign change. EQU a. Fx=Fy=0.5y.sub.0 +y.sub.1 -y.sub.3 [ 4] EQU b. Fw=0.5y.sub.0 +y.sub.1 -0.5y.sub.3 +0.5y.sub.4 [ 5]
y.sub.0, y.sub.1, y.sub.2, y.sub.3 and y.sub.4 are sequential code rate sample values. The linear equations Fx, Fy and Fw have sample values that are multiplied by coefficients which maximize the detection threshold between all possible signal waveform patterns and their minimum distance error waveforms. For example, each decision function (Fx, Fy, etc.) can be represented by the following equation: ##EQU2## where c.sub.i are the coefficients chosen to maximize detection, and k is the number of samples used in the ML detection scheme.
From equation [6], it can be shown that each decision equation has the same form as an FIR filter. Therefore, the detected noise and the detector noise bandwidth are affected by the decision function. Further, in the prior art, decision functions are designed under the assumption that the noise at the sampled input of the detector is additive white Gaussian noise (AWGN). However, partial response channels comprise filter and equalizer components for shaping the input waveform to the target PR pulse. The PR equalizer, in particular, typically supplies high frequency boost to provide pulse-slimming of the input pulse.
The filter and equalizer components in the PR channel shape the noise of the system in the same manner as the input pulse, thereby coloring, or correlating, the input noise according to the filter and equalizer frequency response functions. The target pulse signal at the input of the detector thus contains a noise component that is no longer white in nature, but has an effective noise bandwidth. For this reason, performance of the decision functions within the detector is reduced due to the correlation of noise. A partial response channel is desired that achieves optimum decision performance in the presence of colored noise.